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We show that the problem of finding an optimal schedule for a set of jobs is polynomial complete even in the following two restricted cases. (1) All jobs require one time unit. (2) All jobs require one or two time units, and there are only two processors. As a consequence, the general preemptive scheduling problem is also polynomial complete. These results are tantamount to showing that the scheduling problems mentioned are intractable.
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Jeffrey D. Ullman (1973) studied this question.
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